Show that the partition function ZAB of two independent distinguishable systems A and B both in equilibrium with a heat bath at temperature T equals the product of the partition functions of the separate systems:ZAB = ZAZB

An alien spaceship is 500 m above the ground and moving at a constant velocity of 150 m/s upwards. how high above the ground is the ship after 5 seconds?

22. the top of a cliff is located a distance h above the ground. at a distance h/2 there is a branch that juts out from the side of the cliff, and on this branch a bird's nest is located. two children throw stones at the nest with the same initial speed, one stone straight downward from the top of the cliff and the other stone straight upward from the ground. in the absence of air resistance, which stone hits the nest in the least amount of time?

Aphase diagram assumes is kept constant.